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Keras Constant Input Layers with Fixed Source of Stochasticity

Comments

In [1]:
%matplotlib notebook
In [2]:
import numpy as np
import keras.backend as K

from keras.layers import Input, Activation, Add, GaussianNoise
from keras.models import Sequential, Model

Using TensorFlow backend.

Rationale

TODO

In [3]:
random_tensor = K.random_normal(shape=(8, 3), seed=42)
In [4]:
K.eval(random_tensor)
Out[4]:
array([[-0.28077507, -0.13775212, -0.67632961],
       [ 0.02458041, -0.89358455, -0.82847327],
       [ 1.2068944 ,  1.38101566, -1.45579767],
       [-0.24621388, -1.36084056,  1.08796036],
       [-0.35116589, -0.51385337,  3.41172075],
       [ 0.05885483,  0.89180237, -0.7528832 ],
       [-0.4335728 ,  2.45385313,  0.31374422],
       [-0.52736205,  0.85249925, -0.5379132 ]], dtype=float32)
In [5]:
K.eval(random_tensor)
Out[5]:
array([[ 0.36944136, -0.06497762,  1.05423534],
       [ 0.92629176,  0.45142221,  0.6538806 ],
       [ 0.00987345, -0.75727743,  1.19744813],
       [ 0.10721783, -1.34733653,  0.69856125],
       [ 1.34215105,  0.19264366, -0.02015864],
       [ 0.61278504,  0.43748191,  1.21581125],
       [ 0.42827308, -1.2276696 , -2.39826727],
       [-0.21679108,  0.05826041,  0.10147382]], dtype=float32)
In [6]:
x = Input(shape=(784,))
eps = Input(tensor=K.random_normal(shape=(K.shape(x)[0], 3), seed=42))
In [7]:
try:
    m = Model(x, eps)
except RuntimeError as e:
    print(e)

Graph disconnected: cannot obtain value for tensor Tensor("random_normal_1:0", shape=(?, 3), dtype=float32) at layer "input_2". The following previous layers were accessed without issue: []
In [8]:
m = Model([x, eps], eps)
In [9]:
m.predict(np.ones((8, 784)))
Out[9]:
array([[-0.28077507, -0.13775212, -0.67632961],
       [ 0.02458041, -0.89358455, -0.82847327],
       [ 1.2068944 ,  1.38101566, -1.45579767],
       [-0.24621388, -1.36084056,  1.08796036],
       [-0.35116589, -0.51385337,  3.41172075],
       [ 0.05885483,  0.89180237, -0.7528832 ],
       [-0.4335728 ,  2.45385313,  0.31374422],
       [-0.52736205,  0.85249925, -0.5379132 ]], dtype=float32)
In [10]:
m.predict([np.ones((8, 784))])
Out[10]:
array([[ 0.36944136, -0.06497762,  1.05423534],
       [ 0.92629176,  0.45142221,  0.6538806 ],
       [ 0.00987345, -0.75727743,  1.19744813],
       [ 0.10721783, -1.34733653,  0.69856125],
       [ 1.34215105,  0.19264366, -0.02015864],
       [ 0.61278504,  0.43748191,  1.21581125],
       [ 0.42827308, -1.2276696 , -2.39826727],
       [-0.21679108,  0.05826041,  0.10147382]], dtype=float32)
In [11]:
try:
    m.predict([np.ones((8, 784)), np.ones((8, 3))])
except ValueError as e:
    print(e)

Error when checking model : the list of Numpy arrays that you are passing to your model is not the size the model expected. Expected to see 1 array(s), but instead got the following list of 2 arrays: [array([[ 1.,  1.,  1., ...,  1.,  1.,  1.],
       [ 1.,  1.,  1., ...,  1.,  1.,  1.],
       [ 1.,  1.,  1., ...,  1.,  1.,  1.],
       ..., 
       [ 1.,  1.,  1., ...,  1.,  1.,  1.],
       [ 1...

Working with Pandas MultiIndex Dataframes: Reading and Writing to CSV and HDF5

Comments

In [1]:
%matplotlib notebook
In [2]:
import numpy as np
import pandas as pd

import matplotlib.pyplot as plt

Rationale

For some certain loss functions, such the the negative evidence lower bound (NELBO) in variational inference, they are generally analytically intractable and thus unavailable in closed-form. As such, we might need to resort to taking stochastic estimates of the loss function. In these situations, it is very important to study and understand the robustness of the estimations we are making, particularly in terms of bias and variance. When proposing a new estimator, we may be interested in evaluating the loss at a fined-grained level - not only per batch, but perhaps even per data-point.

This notebook explores storing the recorded losses in Pandas Dataframes. The recorded losses are 3d, with dimensions corresponding to epochs, batches, and data-points. Specifically, they are of shape (n_epochs, n_batches, batch_size). Instead of using the deprecated Panel functionality from Pandas, we explore the preferred MultiIndex Dataframe.

Lastly, we play around with various data serialization formats supported out-of-the-box by Pandas. This might be useful if the training is GPU-intensive, so the script runs and records the loss remotely on a supercomputer, and we must write the results to file, download them and finally analyze them locally. This is usually trivial, but it is unclear what the behaviour is for more complex MultiIndex dataframes. We restrict our attention to the CSV format, which is human-friendly but very slow and inefficient, and the HDF5, which is basically diametrically opposed - it's basically completely inscrutable, but is very fast and takes up laess space.

Synthetic Data

In [3]:
# create some noise
a = np.random.randn(50, 600, 100)
a.shape
Out[3]:
(50, 600, 100)
In [4]:
# create some noise with higher variance and add bias.
b = 2. * np.random.randn(*a.shape) + 1.
b.shape
Out[4]:
(50, 600, 100)
In [5]:
# manufacture some loss function
# there are n_epochs * n_batchs * batch_size 
# recorded values of the loss
loss = 10 / np.linspace(1, 100, a.size)
loss.shape
Out[5]:
(3000000,)

MultiIndex Dataframe

In [6]:
# we will create the indices from the 
# product of these iterators
list(map(range, a.shape))
Out[6]:
[range(0, 50), range(0, 600), range(0, 100)]
In [7]:
# create the MultiIndex
index = pd.MultiIndex.from_product(
    list(map(range, a.shape)), 
    names=['epoch', 'batch', 'datapoint']
)
In [8]:
# create the dataframe that records the two losses
df = pd.DataFrame(
    dict(loss1=loss+np.ravel(a), 
         loss2=loss+np.ravel(b)), 
    index=index
)
df
Out[8]:
loss1 loss2
epoch batch datapoint
0 0 0 10.837250 10.228649
1 9.383650 9.601012
2 9.102928 12.792865
3 9.149701 11.307185
4 9.181607 9.905578
5 8.984361 11.646015
6 8.935352 10.793933
7 9.273609 9.421425
8 10.846009 9.916008
9 10.288851 7.250876
10 10.360709 10.911360
11 9.514765 7.339939
12 9.922280 10.494360
13 9.094041 13.302492
14 9.693384 12.187093
15 9.675839 13.418631
16 11.502391 9.470244
17 10.958843 12.709454
18 10.819225 11.700684
19 9.412562 10.272870
20 10.424428 10.477799
21 9.009290 13.920663
22 8.127529 13.179637
23 8.939673 13.091603
24 8.064599 7.311483
25 9.924553 15.597797
26 8.572734 14.338683
27 10.294223 7.761236
28 11.191123 8.993673
29 9.424269 12.067344
... ... ... ... ...
49 599 70 1.975951 2.746047
71 1.169242 4.194400
72 0.248216 0.730370
73 -0.271330 0.415903
74 -0.888580 0.208060
75 -0.624063 1.081515
76 -1.422904 0.398015
77 0.332523 1.892470
78 -0.224471 -2.839332
79 0.405337 0.266035
80 0.223712 5.810484
81 -0.508689 7.535930
82 -1.915472 -0.275332
83 -0.597498 2.799929
84 -0.443378 2.202897
85 0.610826 1.825950
86 0.305465 0.757416
87 -1.139339 3.221787
88 -1.893639 0.520711
89 -0.286300 3.112420
90 1.268100 1.341298
91 0.251563 1.040859
92 0.083156 1.311108
93 -0.554107 8.272526
94 -2.415105 2.607663
95 0.335266 2.038404
96 0.554412 2.200551
97 0.392182 1.444542
98 -0.252059 1.641488
99 -0.070091 1.490349

3000000 rows × 2 columns

Visualization

In this contrived scenario, loss2 is more biased and has higher variance.

In [9]:
# some basic plotting
fig, ax = plt.subplots()

df.groupby(['epoch', 'batch']).mean().plot(ax=ax)

plt.show()

CSV Read/Write

In [10]:
%%time

df.to_csv('losses.csv')

CPU times: user 9.56 s, sys: 184 ms, total: 9.74 s
Wall time: 13.3 s
In [11]:
!ls -lh losses.csv

-rwxrwxrwx 1 tiao tiao 138M Nov  8 03:14 losses.csv
In [12]:
%%time

df_from_csv = pd.read_csv('losses.csv', index_col=['epoch', 'batch', 'datapoint'], float_precision='high')

/home/tiao/.virtualenvs/anmoku/lib/python3.5/site-packages/numpy/lib/arraysetops.py:463: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  mask |= (ar1 == a)

CPU times: user 1.47 s, sys: 108 ms, total: 1.58 s
Wall time: 3.73 s
In [13]:
# does not recover exactly due to insufficient floating point precision
df_from_csv.equals(df)
Out[13]:
False
In [14]:
# but it has recovered it up to some tiny epsilon
((df-df_from_csv)**2 < 1e-25).all()
Out[14]:
loss1    True
loss2    True
dtype: bool

HDF5 Read/Write

HDF5 writing is orders of magnitude faster.

In [15]:
%%time

df.to_hdf('store.h5', key='losses')

CPU times: user 44 ms, sys: 72 ms, total: 116 ms
Wall time: 720 ms

Furthermore, the file sizes are significantly smaller.

In [16]:
!ls -lh store.h5

-rwxrwxrwx 1 tiao tiao 58M Nov  8 03:15 store.h5
In [17]:
%%time

df_from_hdf = pd.read_hdf('store.h5', key='losses')

CPU times: user 28 ms, sys: 28 ms, total: 56 ms
Wall time: 105 ms

Lastly, it is far more numerical precise.

In [18]:
df.equals(df_from_hdf)
Out[18]:
True

Working with Samples of Distributions over Convolutional Kernels

Comments

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
In [2]:
import numpy as np
import tensorflow as tf

import matplotlib.pyplot as plt

from tensorflow.examples.tutorials.mnist import input_data as mnist_data
In [3]:
tf.__version__
Out[3]:
'1.2.1'
In [4]:
sess = tf.InteractiveSession()
In [5]:
mnist = mnist_data.read_data_sets("/home/tiao/Desktop/MNIST")

Extracting /home/tiao/Desktop/MNIST/train-images-idx3-ubyte.gz
Extracting /home/tiao/Desktop/MNIST/train-labels-idx1-ubyte.gz
Extracting /home/tiao/Desktop/MNIST/t10k-images-idx3-ubyte.gz
Extracting /home/tiao/Desktop/MNIST/t10k-labels-idx1-ubyte.gz
In [6]:
# 50 single-channel (grayscale) 28x28 images
x = mnist.train.images[:50].reshape(-1, 28, 28, 1)
x.shape
Out[6]:
(50, 28, 28, 1)
In [7]:
fig, ax = plt.subplots(figsize=(5, 5))

# showing an arbitrarily chosen image
ax.imshow(np.squeeze(x[5], axis=-1), cmap='gray')

plt.show()

Standard 2D Convolution with conv2d

In [8]:
# 32 kernels of size 5x5x1
kernel = tf.truncated_normal([5, 5, 1, 32], stddev=0.1)
kernel.get_shape().as_list()
Out[8]:
[5, 5, 1, 32]
In [9]:
x_conved = tf.nn.conv2d(x, kernel, 
                        strides=[1, 1, 1, 1], 
                        padding='SAME')
x_conved.get_shape().as_list()
Out[9]:
[50, 28, 28, 32]
In [10]:
x_conved[5, ..., 0].eval().shape
Out[10]:
(28, 28)
In [11]:
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

# showing what the 0th filter looks like
ax1.imshow(kernel[..., 0, 0].eval(), cmap='gray')

# show the previous arbitrarily chosen image
# convolved with the 0th filter
ax2.imshow(x_conved[5, ..., 0].eval(), cmap='gray')

plt.show()

Sample from a Distribution over Kernels

In [12]:
# 8x32 kernels of size 5x5x1
kernels = tf.truncated_normal([8, 5, 5, 1, 32], stddev=0.1)
kernels.get_shape().as_list()
Out[12]:
[8, 5, 5, 1, 32]

Approach 1: Map over samples with conv2d

In [13]:
x_tiled = tf.tile(tf.expand_dims(x, 0), [8, 1, 1, 1, 1])
x_tiled.get_shape().as_list()
Out[13]:
[8, 50, 28, 28, 1]
In [19]:
tf.nn.conv2d(x_tiled[0], kernels[0], 
             strides=[1, 1, 1, 1], 
             padding='SAME').get_shape().as_list()
Out[19]:
[50, 28, 28, 32]
In [15]:
x_conved1 = tf.map_fn(lambda args: tf.nn.conv2d(*args, strides=[1, 1, 1, 1], padding='SAME'),
                      elems=(x_tiled, kernels), dtype=tf.float32)
x_conved1.get_shape().as_list()
Out[15]:
[8, 50, 28, 28, 32]

Approach 2: Flattening

In [16]:
kernels_flat = tf.reshape(tf.transpose(kernels, 
                                       perm=(1, 2, 3, 4, 0)), 
                          shape=(5, 5, 1, 32*8))
kernels_flat.get_shape().as_list()
Out[16]:
[5, 5, 1, 256]
In [17]:
x_conved2 = tf.transpose(tf.reshape(tf.nn.conv2d(x, kernels_flat, 
                                                 strides=[1, 1, 1, 1], 
                                                 padding='SAME'), 
                                    shape=(50, 28, 28, 32, 8)), 
                         perm=(4, 0, 1, 2, 3))
x_conved2.get_shape().as_list()
Out[17]:
[8, 50, 28, 28, 32]
In [18]:
tf.reduce_all(tf.equal(x_conved1, x_conved2)).eval()
Out[18]:
True

Variational Inference with Implicit Approximate Inference Models - @fhuszar's Explaining Away Example Pt. 1 (WIP)

Comments

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
In [70]:
import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Add, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook
In [3]:
# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')
In [4]:
np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)
In [5]:
K.tf.__version__
Out[5]:
'1.2.1'
In [6]:
LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60

Bayesian Logistic Regression (Synthetic Data)

In [7]:
z_min, z_max = -5, 5
In [8]:
z1, z2 = np.mgrid[z_min:z_max:300j, z_min:z_max:300j]
In [9]:
z_grid = np.dstack((z1, z2))
z_grid.shape
Out[9]:
(300, 300, 2)
In [10]:
prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)
In [11]:
log_prior = prior.logpdf(z_grid)
log_prior.shape
Out[11]:
(300, 300)
In [13]:
np.allclose(log_prior, 
            -.5*np.sum(z_grid**2, axis=2)/PRIOR_VARIANCE \
            -np.log(2*np.pi*PRIOR_VARIANCE))
Out[13]:
True
In [15]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(z1, z2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)

plt.show()
In [16]:
x = np.array([0, 5, 8, 12, 50])
In [37]:
def log_likelihood(z, x, beta_0=3., beta_1=1.):
    beta = beta_0 + np.sum(beta_1*np.maximum(0, z**3), axis=-1)
    return -np.log(beta) - x/beta
In [44]:
llhs = log_likelihood(z_grid, x.reshape(-1, 1, 1))
llhs.shape
Out[44]:
(5, 300, 300)
In [59]:
fig, axes = plt.subplots(ncols=len(x), nrows=1, figsize=(20, 4))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(z1, z2, llhs[i,::,::], cmap=plt.cm.magma)

    ax.set_xlim(z_min, z_max)
    ax.set_ylim(z_min, z_max)
    
    ax.set_title('$p(x = {{{0}}} \mid z)$'.format(x[i]))
    ax.set_xlabel('$z_1$')    
    
    if not i:
        ax.set_ylabel('$z_2$')

plt.show()
In [60]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(z1, z2, np.sum(llhs, axis=0), 
                cmap=plt.cm.magma)

ax.set_xlabel('$z_1$')
ax.set_ylabel('$z_2$')

ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)

plt.show()
In [61]:
fig, axes = plt.subplots(ncols=len(x), nrows=1, figsize=(20, 4))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(z1, z2,  np.exp(log_prior+llhs[i,::,::]), 
                cmap='magma')

    ax.set_xlim(z_min, z_max)
    ax.set_ylim(z_min, z_max)
    
    ax.set_title('$Zp(z \mid x = {{{0}}})$'.format(x[i]))
    ax.set_xlabel('$z_1$')    
    
    if not i:
        ax.set_ylabel('$z_2$')

plt.show()
In [63]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(z1, z2, 
            np.exp(log_prior+np.sum(llhs, axis=0)), 
            cmap='magma')

ax.set_xlabel('$z_1$')
ax.set_ylabel('$z_2$')

ax.set_xlim(z_min, z_max)
ax.set_ylim(z_min, z_max)

plt.show()

Model Definitions

Density Ratio Estimator (Discriminator) Model

$T_{\psi}(x, z)$

In [84]:
x_input = Input(shape=(1,), name='x')
x_hidden = Dense(10, activation='relu')(x_input)
x_hidden = Dense(20, activation='relu')(x_hidden)
In [85]:
z_input = Input(shape=(LATENT_DIM,), name='z')
z_hidden = Dense(10, activation='relu')(z_input)
z_hidden = Dense(20, activation='relu')(z_hidden)
In [86]:
discrim_hidden = Add()([x_hidden, z_hidden])
discrim_hidden = Dense(10, activation='relu')(discrim_hidden)
discrim_hidden = Dense(20, activation='relu')(discrim_hidden)
discrim_logit = Dense(1, activation=None, 
                       name='logit')(discrim_hidden)
discrim_out = Activation('sigmoid')(discrim_logit)
In [87]:
discriminator = Model(inputs=[x_input, z_input], outputs=discrim_out)
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])
In [88]:
ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discrim_logit)
In [89]:
SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))
Out[89]:
G 140115456278480 x: InputLayerinput:output:(None, 1)(None, 1)140115456277696 dense_17: Denseinput:output:(None, 1)(None, 10)140115456278480->140115456277696 140115452033176 z: InputLayerinput:output:(None, 2)(None, 2)140115453473064 dense_19: Denseinput:output:(None, 2)(None, 10)140115452033176->140115453473064 140115453258048 dense_18: Denseinput:output:(None, 10)(None, 20)140115456277696->140115453258048 140115452043616 dense_20: Denseinput:output:(None, 10)(None, 20)140115453473064->140115452043616 140115531775392 add_8: Addinput:output:[(None, 20), (None, 20)](None, 20)140115453258048->140115531775392 140115452043616->140115531775392 140115531775168 dense_21: Denseinput:output:(None, 20)(None, 10)140115531775392->140115531775168 140115531775504 dense_22: Denseinput:output:(None, 10)(None, 20)140115531775168->140115531775504 140115543993984 logit: Denseinput:output:(None, 20)(None, 1)140115531775504->140115543993984 140115453098640 activation_2: Activationinput:output:(None, 1)(None, 1)140115543993984->140115453098640
In [105]:
np.ones((32, 5)) + np.ones((16, 5))

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-105-a367db8def8f> in <module>()
----> 1 np.ones((32, 5)) + np.ones((16, 5))

ValueError: operands could not be broadcast together with shapes (32,5) (16,5)
In [112]:
z_grid_ratio = ratio_estimator.predict([np.ones((16, 1)), np.ones((32, 2))])
z_grid_ratio.shape
Out[112]:
(16, 1)

Initial density ratio, prior to any training

In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [ ]:
discriminator.evaluate(prior.rvs(size=5), np.zeros(5))

Approximate Inference Model

$z_{\phi}(x, \epsilon)$

Here we only consider

$z_{\phi}(\epsilon)$

$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$

In [ ]:
inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()

The variational parameters $\phi$ are the trainable weights of the approximate inference model

In [ ]:
phi = inference.trainable_weights
phi
In [ ]:
SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))
In [ ]:
w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape
In [ ]:
eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape
In [ ]:
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [ ]:
metrics = discriminator.evaluate(inputs, targets)
In [ ]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [ ]:
metrics
In [ ]:
metrics_dict = dict(zip(discriminator.metrics_names, metrics))
In [ ]:
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

metrics_plots = {k:ax1.plot([], label=k)[0] 
                 for k in ['loss']} # discriminator.metrics_names}

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
Discriminator pre-training
In [ ]:
def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    # Plot Metrics
        
    metrics_dict = dict(zip(discriminator.metrics_names, metrics))

    for metric in metrics_plots:
        metrics_plots[metric].set_xdata(np.append(metrics_plots[metric].get_xdata(), 
                                                  epoch_num))    
        metrics_plots[metric].set_ydata(np.append(metrics_plots[metric].get_ydata(), 
                                                  metrics_dict[metric]))
        metrics_plots[metric].set_label('{} ({:.2f})' \
                                        .format(metric, 
                                                metrics_dict[metric]))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(**metrics_dict)

    return list(metrics_plots.values())
In [ ]:
# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()
In [ ]:
HTML(anim_html5_video)
In [ ]:
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))
In [ ]:
metrics = discriminator.evaluate(inputs, targets)
In [ ]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()

Evidence lower bound

In [ ]:
def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)
In [ ]:
y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred
In [ ]:
y_true = K.ones((300, 300, 1))*K.constant(y)
y_true
In [ ]:
llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)
In [ ]:
sess = K.get_session()
In [ ]:
np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()

Reweight likelihood term!

In [ ]:
def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(2.*log_likelihood-kl_estimate, axis=-1)

    return elbo
In [ ]:
elbo = make_elbo(ratio_estimator)
In [ ]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [ ]:
inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)
In [ ]:
inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))
In [ ]:
eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
In [ ]:
y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true
In [ ]:
sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))
In [ ]:
inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))

Adversarial Training

In [ ]:
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
In [ ]:
def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training
        
    set_trainable(discriminator, True)

    for _ in tnrange(3*50, unit='step', desc='discriminator', 
                     leave=False):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

    metrics_dict_discrim = dict(zip(discriminator.metrics_names, 
                                    np.atleast_1d(metrics_discrim)))
    
    ## Inference model training
    
    set_trainable(ratio_estimator, False)

    y_tiled = np.tile(y, reps=(BATCH_SIZE, 1))

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, y_tiled)
        
    metrics_dict_inference = dict(zip(inference.metrics_names, 
                                      np.atleast_1d(metrics_inference)))

    global_epoch += 1
    
    # Plot Loss
 
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(),
                                            global_epoch))
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), 
                                            metrics_dict_inference['loss']))

    loss_plot_inference.set_label('inference ({:.2f})' \
                                  .format(metrics_dict_inference['loss']))

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(),
                                          global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(),
                                          metrics_dict_discrim['loss']))

    loss_plot_discrim.set_label('discriminator ({:.2f})' \
                                  .format(metrics_dict_discrim['loss']))
    
    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_inference=metrics_dict_inference['loss'],
                         loss_discriminator=metrics_dict_discrim['loss'])

    return loss_plot_inference, loss_plot_discrim
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)
In [ ]:
with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)

Evaluating the model

In [ ]:
w_sample_prior = prior.rvs(size=128)
eps = np.random.randn(256, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(128), np.ones(256)))
In [ ]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [ ]:
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
In [ ]:
eps = np.random.randn(5000, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
In [ ]:
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*inference.predict(eps[::10]).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

sns.kdeplot(*inference.predict(eps).T,
            cmap='magma', ax=ax2)

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()

Variational Inference with Implicit Approximate Inference Models (WIP Pt. 9)

Comments

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'svg'
In [2]:
import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook

Using TensorFlow backend.
In [3]:
# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')
In [4]:
np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)
In [5]:
K.tf.__version__
Out[5]:
'1.2.1'
In [6]:
LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60

Bayesian Logistic Regression (Synthetic Data)

In [7]:
w_min, w_max = -5, 5
In [8]:
w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]
In [9]:
w_grid = np.dstack((w1, w2))
w_grid.shape
Out[9]:
(300, 300, 2)
In [10]:
prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)
In [11]:
log_prior = prior.logpdf(w_grid)
log_prior.shape
Out[11]:
(300, 300)
In [12]:
log_prior = -np.sum(w_grid**2, axis=2)/2/PRIOR_VARIANCE
log_prior.shape
Out[12]:
(300, 300)
In [13]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [14]:
x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])
In [15]:
X = np.vstack((x1, x2, x3))
X.shape
Out[15]:
(3, 2)
In [16]:
y1 = 1
y2 = 1
y3 = 0
In [17]:
y = np.stack((y1, y2, y3))
y.shape
Out[17]:
(3,)
In [18]:
def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))
In [19]:
llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape
Out[19]:
(300, 300, 3)
In [20]:
fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()
In [21]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [22]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()

Model Definitions

Density Ratio Estimator (Discriminator) Model

$T_{\psi}(x, z)$

Here we consider

$T_{\psi}(w)$

$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$

In [23]:
discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])
In [24]:
ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)
In [25]:
SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))
Out[25]:
G 140532566838016 dense_1_input: InputLayerinput:output:(None, 2)(None, 2)140532566553712 dense_1: Denseinput:output:(None, 2)(None, 10)140532566838016->140532566553712 140532566554384 dense_2: Denseinput:output:(None, 10)(None, 20)140532566553712->140532566554384 140532629958784 logit: Denseinput:output:(None, 20)(None, 1)140532566554384->140532629958784 140532567508640 activation_1: Activationinput:output:(None, 1)(None, 1)140532629958784->140532567508640
In [26]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

Initial density ratio, prior to any training

In [27]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [28]:
discriminator.evaluate(prior.rvs(size=5), np.zeros(5))

5/5 [==============================] - 0s
Out[28]:
[1.0519158840179443, 0.0]

Approximate Inference Model

$z_{\phi}(x, \epsilon)$

Here we only consider

$z_{\phi}(\epsilon)$

$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$

In [29]:
inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

The variational parameters $\phi$ are the trainable weights of the approximate inference model

In [30]:
phi = inference.trainable_weights
phi
Out[30]:
[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]
In [31]:
SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))
Out[31]:
G 140532567173216 dense_3_input: InputLayerinput:output:(None, 3)(None, 3)140532566249824 dense_3: Denseinput:output:(None, 3)(None, 10)140532567173216->140532566249824 140532566253408 dense_4: Denseinput:output:(None, 10)(None, 20)140532566249824->140532566253408 140532567137752 dense_5: Denseinput:output:(None, 20)(None, 2)140532566253408->140532567137752
In [32]:
w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape
Out[32]:
(200, 2)
In [33]:
eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape
Out[33]:
(200, 2)
In [34]:
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))
In [35]:
fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()
In [36]:
metrics = discriminator.evaluate(inputs, targets)

 32/400 [=>............................] - ETA: 0s
In [37]:
w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)
In [38]:
metrics
Out[38]:
[0.72763251781463623, 0.60250000000000004]
In [39]:
metrics_dict = dict(zip(discriminator.metrics_names, metrics))
In [40]:
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

metrics_plots = {k:ax1.plot([], label=k)[0] 
                 for k in ['loss']} # discriminator.metrics_names}

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()
Discriminator pre-training
In [41]:
def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    # Plot Metrics
        
    metrics_dict = dict(zip(discriminator.metrics_names, metrics))

    for metric in metrics_plots:
        metrics_plots[metric].set_xdata(np.append(metrics_plots[metric].get_xdata(), 
                                                  epoch_num))    
        metrics_plots[metric].set_ydata(np.append(metrics_plots[metric].get_ydata(), 
                                                  metrics_dict[metric]))
        metrics_plots[metric].set_label('{} ({:.2f})' \
                                        .format(metric, 
                                                metrics_dict[metric]))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(**metrics_dict)

    return list(metrics_plots.values())
In [42]:
# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()

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In [43]:



    


HTML(anim_html5_video)




















Out[43]:

























In [44]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [45]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [46]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [47]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [48]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [49]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [50]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[50]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [51]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[51]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [52]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [53]:



    


sess = K.get_session()

















In [54]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[54]:








True



















In [55]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [56]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)
    
    return elbo

















In [57]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [58]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(inference_loss(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [59]:



    


inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))

















In [60]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [61]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[61]:








<tf.Tensor 'concat:0' shape=(200, 3) dtype=float32>



















In [62]:



    


sess.run(K.mean(inference_loss(y_true, inference(K.constant(eps))), axis=-1))




















Out[62]:








3.8003495



















In [63]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/200 [===>..........................] - ETA: 0s










Out[63]:








3.8003493118286134

























Adversarial Training













In [64]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [65]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training
        
    set_trainable(discriminator, True)

    for _ in tnrange(3*50, unit='step', desc='discriminator', 
                     leave=False):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

    metrics_dict_discrim = dict(zip(discriminator.metrics_names, 
                                    np.atleast_1d(metrics_discrim)))
    
    ## Inference model training

    set_trainable(ratio_estimator, False)

    y_tiled = np.tile(y, reps=(BATCH_SIZE, 1))

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, y_tiled)

    metrics_dict_inference = dict(zip(inference.metrics_names, 
                                      np.atleast_1d(metrics_inference)))

    global_epoch += 1
    
    # Plot Loss
 
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(),
                                            global_epoch))
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), 
                                            metrics_dict_inference['loss']))

    loss_plot_inference.set_label('inference ({:.2f})' \
                                  .format(metrics_dict_inference['loss']))

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(),
                                          global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(),
                                          metrics_dict_discrim['loss']))

    loss_plot_discrim.set_label('discriminator ({:.2f})' \
                                  .format(metrics_dict_discrim['loss']))
    
    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_inference=metrics_dict_inference['loss'],
                         loss_discriminator=metrics_dict_discrim['loss'])

    return loss_plot_inference, loss_plot_discrim

















In [66]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[66]:

























In [67]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[67]:

























In [68]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[68]:

























In [69]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Out[69]:































Evaluating the model













In [70]:



    


w_sample_prior = prior.rvs(size=128)
eps = np.random.randn(256, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(128), np.ones(256)))

















In [71]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [72]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [73]:



    


eps = np.random.randn(5000, NOISE_DIM)
w_sample_posterior = inference.predict(eps)

















In [74]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*inference.predict(eps[::10]).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

sns.kdeplot(*inference.predict(eps).T,
            cmap='magma', ax=ax2)

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [75]:



    


output = expit(np.random.randn(256))
target = np.hstack((np.zeros(128), np.ones(128)))

















In [76]:



    


2*K.mean(K.binary_crossentropy(output=K.constant(output), 
                      target=K.constant(target))).eval(session=sess)




















Out[76]:








1.5870189666748047



















In [77]:



    


np.mean(-np.log(output[128:])-np.log(1-output[:128]))




















Out[77]:








1.5870191065045991



















In [78]:



    


(-np.log(output[:128])-np.log(1-output[128:])).shape




















Out[78]:








(128,)



















In [79]:



    


p1[:128][0]


























---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-79-3424496d14cb> in <module>()
----> 1 p1[:128][0]

NameError: name 'p1' is not defined


















In [ ]:



    


p1[128:][0]

















In [ ]:



    


ratio_estimator.get_weights()[0]












    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 8)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook


























Using TensorFlow backend.



















In [3]:



    


# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
139996050319736
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)139996049881464
dense_1: Denseinput:output:(None, 2)(None, 10)139996050319736->139996049881464
139996049882416
dense_2: Denseinput:output:(None, 10)(None, 20)139996049881464->139996049882416
139996050321304
logit: Denseinput:output:(None, 20)(None, 1)139996049882416->139996050321304
139996050741624
activation_1: Activationinput:output:(None, 1)(None, 1)139996050321304->139996050741624



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.62235820293426514, 0.60000002384185791]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
139996049667352
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)139996049443528
dense_3: Denseinput:output:(None, 3)(None, 10)139996049667352->139996049443528
139996049443416
dense_4: Denseinput:output:(None, 10)(None, 20)139996049443528->139996049443416
139996049667520
dense_5: Denseinput:output:(None, 20)(None, 2)139996049443416->139996049667520



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(200, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(200, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


metrics




















Out[37]:








[0.69308857917785649, 0.47749999999999998]



















In [38]:



    


metrics_dict = dict(zip(discriminator.metrics_names, metrics))

















In [39]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

metrics_plots = {k:ax1.plot([], label=k)[0] 
                 for k in ['loss']} # discriminator.metrics_names}

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()



















































Discriminator pre-training













In [40]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    # Plot Metrics
        
    metrics_dict = dict(zip(discriminator.metrics_names, metrics))

    for metric in metrics_plots:
        metrics_plots[metric].set_xdata(np.append(metrics_plots[metric].get_xdata(), 
                                                  epoch_num))    
        metrics_plots[metric].set_ydata(np.append(metrics_plots[metric].get_ydata(), 
                                                  metrics_dict[metric]))
        metrics_plots[metric].set_label('{} ({:.2f})' \
                                        .format(metric, 
                                                metrics_dict[metric]))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(**metrics_dict)

    return list(metrics_plots.values())

















In [41]:



    


# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()


























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In [42]:



    


HTML(anim_html5_video)




















Out[42]:

























In [43]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [44]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [45]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [46]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

metrics_dict = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**metrics_dict), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [47]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [48]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[48]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [49]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[49]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [50]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [51]:



    


sess = K.get_session()

















In [52]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[52]:








True



















In [53]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [54]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [55]:



    


elbo = make_elbo(ratio_estimator)

















In [56]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [57]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [58]:



    


inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))

















In [59]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [60]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[60]:








<tf.Tensor 'concat:0' shape=(200, 3) dtype=float32>



















In [61]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[61]:








-2.5127466



















In [62]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/200 [===>..........................] - ETA: 0s










Out[62]:








2.5127464294433595

























Adversarial Training













In [63]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

loss_plot_inference, = ax1.plot([], label='inference')
loss_plot_discrim, = ax1.plot([], label='discriminator')

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [64]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, loss_plot_inference, loss_plot_discrim
    
    # Single training epoch

    ## Ratio estimator training
        
    set_trainable(discriminator, True)

    for _ in tnrange(3*50, unit='step', desc='discriminator', 
                     leave=False):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

    metrics_dict_discrim = dict(zip(discriminator.metrics_names, 
                                    np.atleast_1d(metrics_discrim)))
    
    ## Inference model training
    
    set_trainable(ratio_estimator, False)

    y_tiled = np.tile(y, reps=(BATCH_SIZE, 1))

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, y_tiled)
        
    metrics_dict_inference = dict(zip(inference.metrics_names, 
                                      np.atleast_1d(metrics_inference)))

    global_epoch += 1
    
    # Plot Loss
 
    loss_plot_inference.set_xdata(np.append(loss_plot_inference.get_xdata(),
                                            global_epoch))
    loss_plot_inference.set_ydata(np.append(loss_plot_inference.get_ydata(), 
                                            metrics_dict_inference['loss']))

    loss_plot_inference.set_label('inference ({:.2f})' \
                                  .format(metrics_dict_inference['loss']))

    loss_plot_discrim.set_xdata(np.append(loss_plot_discrim.get_xdata(),
                                          global_epoch))
    loss_plot_discrim.set_ydata(np.append(loss_plot_discrim.get_ydata(),
                                          metrics_dict_discrim['loss']))

    loss_plot_discrim.set_label('discriminator ({:.2f})' \
                                  .format(metrics_dict_discrim['loss']))
    
    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss_inference=metrics_dict_inference['loss'],
                         loss_discriminator=metrics_dict_discrim['loss'])

    return loss_plot_inference, loss_plot_discrim

















In [65]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Out[65]:

























In [66]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Out[66]:

























In [67]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Out[67]:

























In [68]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Out[68]:































Evaluating the model













In [81]:



    


w_sample_prior = prior.rvs(size=128)
eps = np.random.randn(256, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(128), np.ones(256)))

















In [82]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [85]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [101]:



    


eps = np.random.randn(5000, NOISE_DIM)
w_sample_posterior = inference.predict(eps)

















In [105]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*inference.predict(eps[::10]).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

sns.kdeplot(*inference.predict(eps).T,
            cmap='magma', ax=ax2)

plt.show()








































    

  


    

    
Variational Inference with Implicit Models (forked from @fhuszar)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import theano

import matplotlib.pyplot as plt
import seaborn as sns

from collections import defaultdict

from scipy.special import expit
from scipy.stats import logistic

from theano import tensor as T
from theano.tensor.shared_randomstreams import RandomStreams
from theano.printing import debugprint

from lasagne.updates import adam
from lasagne.utils import floatX
from lasagne.nonlinearities import sigmoid
from lasagne.layers import get_output, get_all_params
from lasagne.layers import (InputLayer,
                            DenseLayer,
                            NonlinearityLayer)


from matplotlib.animation import FuncAnimation
from IPython.display import HTML, SVG, display_html
from tqdm import tnrange, tqdm_notebook


























/home/tiao/.virtualenvs/implicit/lib/python3.5/site-packages/theano/tensor/signal/downsample.py:6: UserWarning: downsample module has been moved to the theano.tensor.signal.pool module.
  "downsample module has been moved to the theano.tensor.signal.pool module.")



















In [3]:



    


# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3
PRETRAIN_EPOCHS = 60

















In [6]:



    


w_min, w_max = -5, 5

















In [7]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [8]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[8]:








(300, 300, 2)



















In [9]:



    


log_prior = -.5*np.sum(w_grid**2, axis=2)/PRIOR_VARIANCE
log_prior.shape




















Out[9]:








(300, 300)



















In [10]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [11]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])

















In [12]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[12]:








(3, 2)



















In [13]:



    


y1 = 1
y2 = 1
y3 = -1

















In [14]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[14]:








(3,)



















In [15]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return logistic.logcdf(y*(np.dot(w.T,x)))

















In [16]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[16]:








(300, 300, 3)



















In [17]:



    


fig, axes = plt.subplots(ncols=3, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [18]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [19]:



    


# unnormalised log posterior
# only for illustration purposes
log_post = log_prior + np.sum(llhs, axis=2)

















In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.exp(log_post), cmap='magma')
ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Fitting an approximate posterior



This part is for the actual GAN stuff. Here we define the generator and the discriminator networks in Lasagne, and code up the two loss functions in theano.













In [21]:



    


#defines a 'generator' network
def build_G(input_var=None, num_z = 3):
    
    network = InputLayer(input_var=input_var, shape=(None, num_z))
    
    network = DenseLayer(incoming = network, num_units=10)
    
    network = DenseLayer(incoming = network, num_units=20)
    
    network = DenseLayer(incoming = network, num_units=2, nonlinearity=None)
    
    return network

















In [22]:



    


#defines the 'discriminator network'
def build_D(input_var=None):

    network = InputLayer(input_var=input_var, shape = (None, 2))
    
    network = DenseLayer(incoming = network, num_units=10)
    
    network = DenseLayer(incoming = network, num_units=20)
    
    network = DenseLayer(incoming = network, num_units=1, nonlinearity=None)
    
    normalised = NonlinearityLayer(incoming = network, nonlinearity = sigmoid)
    
    return { 'unnorm':network, 'norm':normalised }

















In [23]:



    


#variables for input (design matrix), output labels, GAN noise variable, weights
x_var = T.matrix('design matrix')
y_var = T.vector('labels')
z_var = T.matrix('GAN noise')
w_var = T.matrix('weights')

#theano variables for things like batchsize, learning rate, etc.
batchsize_var = T.scalar('batchsize', dtype='int32')
prior_variance_var = T.scalar('prior variance')
learningrate_var = T.scalar('learning rate')

#random numbers for sampling from the prior or from the GAN
srng = RandomStreams(seed=13574437)
z_rnd = srng.normal((batchsize_var,3))
prior_rnd = srng.normal((batchsize_var,2))

#instantiating the G and D networks
generator = build_G(z_var)
discriminator = build_D()

#these expressions are random samples from the generator and the prior, respectively
samples_from_grenerator = get_output(generator, z_rnd)
samples_from_prior = prior_rnd*T.sqrt(prior_variance_var)

#discriminator output for synthetic samples, both normalised and unnormalised (after/before sigmoid)
D_of_G = get_output(discriminator['norm'], inputs=samples_from_grenerator)
s_of_G = get_output(discriminator['unnorm'], inputs=samples_from_grenerator)

#discriminator output for real samples from the prior
D_of_prior = get_output(discriminator['norm'], inputs=samples_from_prior)

#loss of discriminator - simple binary cross-entropy loss
loss_D = -T.log(D_of_G).mean() - T.log(1-D_of_prior).mean()

#log likelihood for each synthetic w sampled from the generator
log_likelihood = T.log(
    T.nnet.sigmoid(
        (y_var.dimshuffle(0,'x','x')*(x_var.dimshuffle(0,1,'x') * samples_from_grenerator.dimshuffle('x', 1, 0))).sum(1)
    )
).sum(0).mean()

#loss for G is the sum of unnormalised discriminator output and the negative log likelihood
loss_G = s_of_G.mean() - log_likelihood

#compiling theano functions:
evaluate_generator = theano.function(
    [z_var],
    get_output(generator),
    allow_input_downcast=True
)

sample_generator = theano.function(
    [batchsize_var],
    samples_from_grenerator,
    allow_input_downcast=True,
)

sample_prior = theano.function(
    [prior_variance_var, batchsize_var],
    samples_from_prior,
    allow_input_downcast=True
)

params_D = get_all_params(discriminator['norm'], trainable=True)

updates_D = adam(
    loss_D,
    params_D,
    learning_rate = learningrate_var
)

train_D = theano.function(
    [learningrate_var, batchsize_var, prior_variance_var],
    loss_D,
    updates = updates_D,
    allow_input_downcast = True
)

params_G = get_all_params(generator, trainable=True)

updates_G = adam(
    loss_G,
    params_G,
    learning_rate = learningrate_var
)

train_G = theano.function(
    [x_var, y_var, learningrate_var, batchsize_var],
    loss_G,
    updates = updates_G,
    allow_input_downcast = True
)

evaluate_discriminator = theano.function(
    [w_var],
    get_output([discriminator['unnorm'],discriminator['norm']],w_var),
    allow_input_downcast = True
)

#this is to evaluate the log-likelihood of an arbitrary set of w
llh_for_w = T.nnet.sigmoid((y_var.dimshuffle(0,'x','x')*(x_var.dimshuffle(0,1,'x') * w_var.dimshuffle('x', 1, 0))).sum(1))

evaluate_loglikelihood = theano.function(
        [x_var, y_var, w_var],
        llh_for_w,
        allow_input_downcast = True
    )

















In [24]:



    


fig, ax = plt.subplots(figsize=(5, 5))

w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300,300)

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [25]:



    


w_sample_prior = sample_prior(PRIOR_VARIANCE, BATCH_SIZE)
w_sample_posterior = sample_generator(BATCH_SIZE)

















In [26]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [27]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.exp(log_post), cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [28]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

loss_plot, = ax1.plot([], label='loss')

ax1.set_xlabel('epoch')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [29]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, steps_per_epoch=15):

    # Single training epoch
    
    for step in tnrange(steps_per_epoch, unit='step', leave=False):
        
        loss = np.asscalar(train_D(LEARNING_RATE, 
                                   batch_size, 
                                   PRIOR_VARIANCE))
    
    w_sample_prior = sample_prior(PRIOR_VARIANCE, batch_size)
    w_sample_posterior = sample_generator(batch_size)

    inputs = np.vstack((w_sample_prior, w_sample_posterior))
    targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))    
    
    w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300,300)
    
    # Plot Loss

    loss_plot.set_xdata(np.append(loss_plot.get_xdata(), epoch_num))    
    loss_plot.set_ydata(np.append(loss_plot.get_ydata(), loss))
    loss_plot.set_label('loss ({:.2f})'.format(loss))
    
    ax1.set_xlabel('epoch {:2d}'.format(epoch_num))
    ax1.legend(loc='upper left')

    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()
    
    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)
    
    # Progress Bar Updates
    
    prog_bar.update()
    prog_bar.set_postfix(loss=loss)

    return loss_plot,

















In [30]:



    


# main training loop is managed by higher-order
# FuncAnimation which makes calls to an `animate` 
# function that encapsulates the logic of single
# training epoch. Has benefit of producing 
# animation but can incur significant overhead
with tqdm_notebook(total=PRETRAIN_EPOCHS, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=PRETRAIN_EPOCHS,
                         interval=200, # 5 fps
                         blit=True)

    anim_html5_video = anim.to_html5_video()


























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In [31]:



    


HTML(anim_html5_video)




















Out[31]:

























In [32]:



    


fig, ax = plt.subplots(figsize=(5, 5))

w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300,300)

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Adversarial Training













In [33]:



    


llh_theano = evaluate_loglikelihood(X, y, w_grid.reshape(300*300, 2))
llh_theano.shape




















Out[33]:








(3, 90000)



















In [34]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap='magma')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)
ax1.set_title('numpy loglikelihood')

ax2.contourf(w1, w2, np.sum(np.log(llh_theano), 0).reshape(300,300), 
             cmap='magma')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)
ax2.set_title('theano loglikelihood')

plt.show()













































In [35]:



    


np.allclose(np.sum(llhs, axis=2),
            np.sum(np.log(llh_theano), 0).reshape(300,300))




















Out[35]:








True



















In [36]:



    


fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

global_epoch = 0

plots_dict = {k:ax1.plot([], label=k)[0] for k in ('inference', 
                                                   'discriminator', 
                                                   'neg_log_likelihood',
                                                   'kl')}

ax1.set_xlabel('epoch')
ax1.set_ylabel('loss')
ax1.legend(loc='upper left')

ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

plt.show()













































In [37]:



    


def train_animate(epoch_num, prog_bar, batch_size=200, 
                  steps_per_epoch=15):

    global global_epoch, plots_dict

    plot_values = defaultdict(int)
    
    # Single training epoch

    ## Ratio estimator training

    for _ in tnrange(150, unit='step', desc='discriminator', 
                     leave=False):

        plot_values['discriminator'] = np.asscalar(train_D(LEARNING_RATE, 
                                                           batch_size, 
                                                           PRIOR_VARIANCE))
    
    ## Inference model training

    for _ in tnrange(1, unit='step', desc='inference', leave=False):

        np.asscalar(train_G(X, y, LEARNING_RATE, batch_size))

    global_epoch += 1

    w_sample_prior = sample_prior(PRIOR_VARIANCE, batch_size)
    w_sample_posterior = sample_generator(batch_size)

    inputs = np.vstack((w_sample_prior, w_sample_posterior))
    targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

    plot_values['kl'] = np.mean(evaluate_discriminator(w_sample_posterior)[0])
    plot_values['neg_log_likelihood'] = -np.mean(np.sum(np.log(evaluate_loglikelihood(X, y, w_sample_posterior)), axis=0))
    
    plot_values['inference'] = plot_values['kl'] + plot_values['neg_log_likelihood']

    w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300,300)
    
    # Plot Loss

    for k in plots_dict:

        plots_dict[k].set_xdata(np.append(plots_dict[k].get_xdata(), global_epoch))
        plots_dict[k].set_ydata(np.append(plots_dict[k].get_ydata(), plot_values[k]))
        plots_dict[k].set_label('{} ({:.2f})'.format(k, plot_values[k]))

    ax1.set_xlabel('epoch {:2d}'.format(global_epoch))
    ax1.legend(loc='upper left')
    
    ax1.relim()
    ax1.autoscale_view()
    
    # Contour Plot
    
    ax2.cla()

    ax2.contourf(w1, w2, w_grid_ratio, cmap='magma')
    ax2.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    ax2.set_xlabel('$w_1$')
    ax2.set_ylabel('$w_2$')

    ax2.set_xlim(w_min, w_max)
    ax2.set_ylim(w_min, w_max)

    # Progress Bar Updates
    
    prog_bar.update()
#     prog_bar.set_postfix(loss_g=loss_g, loss_d=loss_d)

    return list(plots_dict.values())

















In [38]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[38]:

























In [39]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[39]:

























In [40]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 































Out[40]:

























In [41]:



    


with tqdm_notebook(total=50, 
                   unit='epoch', leave=True) as prog_bar:

    anim = FuncAnimation(fig, 
                         train_animate,
                         fargs=(prog_bar,),
                         frames=50,
                         interval=200, # 5 fps
                         blit=True)
    
    anim_html5_video = anim.to_html5_video()
    
HTML(anim_html5_video)


























Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Widget Javascript not detected.  It may not be installed or enabled properly.

















 
 





















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Out[41]:

























In [42]:



    


w_grid_ratio, _ = evaluate_discriminator(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300,300)

















In [43]:



    


w_sample_prior = sample_prior(PRIOR_VARIANCE, 100)
w_sample_posterior = sample_generator(100)

















In [44]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(100), np.ones(100)))

















In [45]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, w_grid_ratio, cmap='magma')
ax1.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax1.set_xlabel('$w_1$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax1.set_title('estimated log density ratio $\Phi^{-1}(D)$')

ax2.contourf(w1, w2, np.sum(llhs, axis=2), 
             cmap=plt.cm.magma)

ax2.set_xlabel('$w_1$')
ax2.set_ylabel('$w_2$')

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

ax2.set_title('log likelihood')

plt.show()













































In [46]:



    


fig, ax = plt.subplots( figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_post), 
            cmap=plt.cm.magma)

ax.scatter(*sample_generator(1000).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [50]:



    


fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(9, 4))

ax1.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax1.scatter(*sample_generator(100).T, 
            s=4.**2, alpha=.6, cmap='coolwarm_r')

ax1.set_xlabel('$w_1$')
ax1.set_ylabel('$w_2$')

ax1.set_xlim(w_min, w_max)
ax1.set_ylim(w_min, w_max)

ax1.set_title('true posterior')

sns.kdeplot(*sample_generator(5000).T,
            shade=True, cmap='magma', ax=ax2)

ax2.set_xlim(w_min, w_max)
ax2.set_ylim(w_min, w_max)

ax2.set_title('kde of approximate posterior')

plt.show()








































    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 7)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.optimizers import Adam
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import SVG
from tqdm import tnrange


























Using TensorFlow backend.



















In [3]:



    


# display animation inline
plt.rc('animation', html='html5')
plt.style.use('seaborn-notebook')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 200
PRIOR_VARIANCE = 2.
LEARNING_RATE = 3e-3























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([  .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer=Adam(lr=LEARNING_RATE),
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
4729044328
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)4727278616
dense_1: Denseinput:output:(None, 2)(None, 10)4729044328->4727278616
4729043432
dense_2: Denseinput:output:(None, 10)(None, 20)4727278616->4729043432
4729057176
logit: Denseinput:output:(None, 20)(None, 1)4729043432->4729057176
4721891144
activation_1: Activationinput:output:(None, 1)(None, 1)4729057176->4721891144



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.53143018484115601, 1.0]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
4732353784
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)4732435816
dense_3: Denseinput:output:(None, 3)(None, 10)4732353784->4732435816
4732434640
dense_4: Denseinput:output:(None, 10)(None, 20)4732435816->4732434640
4716115280
dense_5: Denseinput:output:(None, 20)(None, 2)4732434640->4716115280



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(200, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(200, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)




















Out[37]:








(-5, 5)










































Discriminator pre-training













In [38]:



    


def train_animate(epoch_num, batch_size=200, steps_per_epoch=15):

    for step in range(steps_per_epoch):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    ax.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

    ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

    train_info = dict(zip(discriminator.metrics_names, metrics))
    train_info['epoch'] = epoch_num
    
    props = dict(boxstyle='round', facecolor='w', alpha=0.5)

    ax.text(0.05, 0.05, 
            ('epoch: {epoch:2d}\n'
             'accuracy: {binary_accuracy:.2f}\n'        
             'loss: {loss:.2f}').format(**train_info), 
            transform=ax.transAxes, bbox=props)

    ax.set_xlabel('$w_1$')
    ax.set_ylabel('$w_2$')

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    return ax

















In [39]:



    


FuncAnimation(fig, train_animate, frames=60, 
              interval=200, # 5 fps
              blit=False)




















Out[39]:

























In [40]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [41]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [42]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [43]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [44]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [45]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[45]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [46]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[46]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [47]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [48]:



    


sess = K.get_session()

















In [49]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[49]:








True



















In [50]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [51]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [52]:



    


elbo = make_elbo(ratio_estimator)

















In [53]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [54]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [55]:



    


inference.compile(loss=inference_loss, 
                  optimizer=Adam(lr=LEARNING_RATE))

















In [56]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [57]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[57]:








<tf.Tensor 'concat:0' shape=(200, 3) dtype=float32>



















In [58]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[58]:








-3.8279114



















In [59]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/200 [===>..........................] - ETA: 0s










Out[59]:








3.8279113578796387

























Training













In [60]:



    


for epoch in tnrange(200, desc='epoch'):

    set_trainable(ratio_estimator, False)

    for _ in tnrange(1, desc='generator'):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, np.tile(y, reps=(BATCH_SIZE, 1)))

    set_trainable(discriminator, True)

    for _ in tnrange(3*50, desc='discriminator'):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)


























 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 





















 
 







































In [61]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [62]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/400 [=>............................] - ETA: 0s


















In [63]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [64]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.gray)

ax.scatter(*inputs.T, c=targets, s=4.**2, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()








































    

  


    

    
Variational Inference with Implicit Approximate Inference Models (WIP Pt. 6)

        

            

            

                
            Comments


        



    

    

    







In [1]:



    


%matplotlib inline
%config InlineBackend.figure_format = 'svg'

















In [2]:



    


import numpy as np
import keras.backend as K

import matplotlib.pyplot as plt
import seaborn as sns

from scipy.stats import logistic, multivariate_normal, norm
from scipy.special import expit

from keras.models import Model, Sequential
from keras.layers import Activation, Dense, Dot, Input
from keras.utils.vis_utils import model_to_dot

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation

from IPython.display import SVG


























Using TensorFlow backend.



















In [3]:



    


plt.style.use('seaborn-notebook')
# display animation inline
plt.rc('animation', html='html5')
sns.set_context('notebook')

















In [4]:



    


np.set_printoptions(precision=2,
                    edgeitems=3,
                    linewidth=80,
                    suppress=True)

















In [5]:



    


K.tf.__version__




















Out[5]:








'1.2.1'



















In [6]:



    


LATENT_DIM = 2
NOISE_DIM = 3
BATCH_SIZE = 128
PRIOR_VARIANCE = 2.























Bayesian Logistic Regression (Synthetic Data)













In [7]:



    


w_min, w_max = -5, 5

















In [8]:



    


w1, w2 = np.mgrid[w_min:w_max:300j, w_min:w_max:300j]

















In [9]:



    


w_grid = np.dstack((w1, w2))
w_grid.shape




















Out[9]:








(300, 300, 2)



















In [10]:



    


prior = multivariate_normal(mean=np.zeros(LATENT_DIM), 
                            cov=PRIOR_VARIANCE)

















In [11]:



    


log_prior = prior.logpdf(w_grid)
log_prior.shape




















Out[11]:








(300, 300)



















In [12]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, log_prior, cmap='magma')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [13]:



    


x1 = np.array([ 1.5,  1.])
x2 = np.array([-1.5,  1.])
x3 = np.array([- .5, -1.])

















In [14]:



    


X = np.vstack((x1, x2, x3))
X.shape




















Out[14]:








(3, 2)



















In [15]:



    


y1 = 1
y2 = 1
y3 = 0

















In [16]:



    


y = np.stack((y1, y2, y3))
y.shape




















Out[16]:








(3,)



















In [17]:



    


def log_likelihood(w, x, y):
    # equiv. to negative binary cross entropy
    return np.log(expit(np.dot(w.T, x)*(-1)**(1-y)))

















In [18]:



    


llhs = log_likelihood(w_grid.T, X.T, y)
llhs.shape




















Out[18]:








(300, 300, 3)



















In [19]:



    


fig, axes = plt.subplots(ncols=3, nrows=1, figsize=(6, 2))
fig.tight_layout()

for i, ax in enumerate(axes):
    
    ax.contourf(w1, w2, llhs[::,::,i], cmap=plt.cm.magma)

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    ax.set_title('$p(y_{{{0}}} \mid x_{{{0}}}, w)$'.format(i+1))
    ax.set_xlabel('$w_1$')    
    
    if not i:
        ax.set_ylabel('$w_2$')

plt.show()













































In [20]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, np.sum(llhs, axis=2), 
                cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [21]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap='magma')

ax.scatter(*X.T, c=y, cmap='coolwarm', marker=',')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Model Definitions



















Density Ratio Estimator (Discriminator) Model



















$T_{\psi}(x, z)$


Here we consider


$T_{\psi}(w)$


$T_{\psi} : \mathbb{R}^2 \to \mathbb{R}$













In [22]:



    


discriminator = Sequential(name='discriminator')
discriminator.add(Dense(10, input_dim=LATENT_DIM, activation='relu'))
discriminator.add(Dense(20, activation='relu'))
discriminator.add(Dense(1, activation=None, name='logit'))
discriminator.add(Activation('sigmoid'))
discriminator.compile(optimizer='adam',
                      loss='binary_crossentropy',
                      metrics=['binary_accuracy'])

















In [23]:



    


ratio_estimator = Model(
    inputs=discriminator.inputs, 
    outputs=discriminator.get_layer(name='logit').output)

















In [24]:



    


SVG(model_to_dot(discriminator, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[24]:






G
4766144608
dense_1_input: InputLayerinput:output:(None, 2)(None, 2)4766145224
dense_1: Denseinput:output:(None, 2)(None, 10)4766144608->4766145224
4767336208
dense_2: Denseinput:output:(None, 10)(None, 20)4766145224->4767336208
4766143992
logit: Denseinput:output:(None, 20)(None, 1)4767336208->4766143992
4766535464
activation_1: Activationinput:output:(None, 1)(None, 1)4766143992->4766535464



















In [25]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)























Initial density ratio, prior to any training













In [26]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [27]:



    


discriminator.evaluate(prior.rvs(size=5), np.zeros(5))


























5/5 [==============================] - 0s











Out[27]:








[0.72363483905792236, 0.40000000596046448]

























Approximate Inference Model



















$z_{\phi}(x, \epsilon)$


Here we only consider


$z_{\phi}(\epsilon)$


$z_{\phi}: \mathbb{R}^3 \to \mathbb{R}^2$













In [28]:



    


inference = Sequential()
inference.add(Dense(10, input_dim=NOISE_DIM, activation='relu'))
inference.add(Dense(20, activation='relu'))
inference.add(Dense(LATENT_DIM, activation=None))
inference.summary()


























_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_3 (Dense)              (None, 10)                40        
_________________________________________________________________
dense_4 (Dense)              (None, 20)                220       
_________________________________________________________________
dense_5 (Dense)              (None, 2)                 42        
=================================================================
Total params: 302
Trainable params: 302
Non-trainable params: 0
_________________________________________________________________

























The variational parameters $\phi$ are the trainable weights of the approximate inference model













In [29]:



    


phi = inference.trainable_weights
phi




















Out[29]:








[<tf.Variable 'dense_3/kernel:0' shape=(3, 10) dtype=float32_ref>,
 <tf.Variable 'dense_3/bias:0' shape=(10,) dtype=float32_ref>,
 <tf.Variable 'dense_4/kernel:0' shape=(10, 20) dtype=float32_ref>,
 <tf.Variable 'dense_4/bias:0' shape=(20,) dtype=float32_ref>,
 <tf.Variable 'dense_5/kernel:0' shape=(20, 2) dtype=float32_ref>,
 <tf.Variable 'dense_5/bias:0' shape=(2,) dtype=float32_ref>]



















In [30]:



    


SVG(model_to_dot(inference, show_shapes=True)
    .create(prog='dot', format='svg'))




















Out[30]:






G
4769765752
dense_3_input: InputLayerinput:output:(None, 3)(None, 3)4769787520
dense_3: Denseinput:output:(None, 3)(None, 10)4769765752->4769787520
4769190184
dense_4: Denseinput:output:(None, 10)(None, 20)4769787520->4769190184
4769949288
dense_5: Denseinput:output:(None, 20)(None, 2)4769190184->4769949288



















In [31]:



    


w_sample_prior = prior.rvs(size=BATCH_SIZE)
w_sample_prior.shape




















Out[31]:








(128, 2)



















In [32]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
w_sample_posterior = inference.predict(eps)
w_sample_posterior.shape




















Out[32]:








(128, 2)



















In [33]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [34]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, 
            np.exp(log_prior+np.sum(llhs, axis=2)), 
            cmap=plt.cm.magma)

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [35]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [36]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [37]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Discriminator pre-training













In [38]:



    


def train_animate(epoch_num, batch_size=128, steps_per_epoch=20):

    for step in range(steps_per_epoch):

        w_sample_prior = prior.rvs(size=batch_size)

        eps = np.random.randn(batch_size, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(batch_size), np.ones(batch_size)))

        metrics = discriminator.train_on_batch(inputs, targets)

    ax.cla()

    w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
    w_grid_ratio = w_grid_ratio.reshape(300, 300)

    ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

    ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

    train_info = dict(zip(discriminator.metrics_names, metrics))
    train_info['epoch'] = epoch_num
    
    props = dict(boxstyle='round', facecolor='w', alpha=0.5)

    ax.text(0.05, 0.05, 
            ('epoch: {epoch:2d}\n'
             'accuracy: {binary_accuracy:.2f}\n'        
             'loss: {loss:.2f}').format(**train_info), 
            transform=ax.transAxes, bbox=props)

    ax.set_xlabel('$w_1$')
    ax.set_ylabel('$w_2$')

    ax.set_xlim(w_min, w_max)
    ax.set_ylim(w_min, w_max)
    
    return ax

















In [39]:



    


FuncAnimation(fig, train_animate, frames=50, 
              interval=200, # 5 fps
              blit=False)




















Out[39]:

























In [40]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [41]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [42]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [43]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()



















































Evidence lower bound













In [44]:



    


def set_trainable(model, trainable):
    """inorder traversal"""
    model.trainable = trainable

    if isinstance(model, Model): # i.e. has layers
        for layer in model.layers:
            set_trainable(layer, trainable)

















In [45]:



    


y_pred = K.sigmoid(K.dot(
    K.constant(w_grid),
    K.transpose(K.constant(X))))
y_pred




















Out[45]:








<tf.Tensor 'Sigmoid:0' shape=(300, 300, 3) dtype=float32>



















In [46]:



    


y_true = K.ones((300, 300, 1))*K.constant(y)
y_true




















Out[46]:








<tf.Tensor 'mul_33:0' shape=(300, 300, 3) dtype=float32>



















In [47]:



    


llhs_keras = - K.binary_crossentropy(
                   y_pred, 
                   y_true, 
                   from_logits=False)

















In [48]:



    


sess = K.get_session()

















In [49]:



    


np.allclose(np.sum(llhs, axis=-1),
            sess.run(K.sum(llhs_keras, axis=-1)))




















Out[49]:








True



















In [50]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(K.sum(llhs_keras, axis=-1)), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [51]:



    


def make_elbo(ratio_estimator):
    
    set_trainable(ratio_estimator, False)
    
    def elbo(y_true, w_sample):
        kl_estimate = ratio_estimator(w_sample)
        y_pred = K.dot(w_sample, K.transpose(K.constant(X)))
        log_likelihood = - K.binary_crossentropy(y_pred, y_true, 
                                                 from_logits=True)
        return K.mean(log_likelihood-kl_estimate, axis=-1)

    return elbo

















In [52]:



    


elbo = make_elbo(ratio_estimator)

















In [53]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, sess.run(elbo(y_true, K.constant(w_grid))), 
            cmap=plt.cm.magma)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()













































In [59]:



    


inference_loss = lambda y_true, w_sample: -make_elbo(ratio_estimator)(y_true, w_sample)

















In [60]:



    


inference.compile(loss=inference_loss, 
                  optimizer='adam')

















In [61]:



    


eps = np.random.randn(BATCH_SIZE, NOISE_DIM)

















In [62]:



    


y_true = K.repeat_elements(K.expand_dims(K.constant(y), axis=0), 
                           axis=0, rep=BATCH_SIZE)
y_true




















Out[62]:








<tf.Tensor 'concat_1:0' shape=(128, 3) dtype=float32>



















In [63]:



    


sess.run(K.mean(elbo(y_true, inference(K.constant(eps))), axis=-1))




















Out[63]:








-3.9920437



















In [64]:



    


inference.evaluate(eps, np.tile(y, reps=(BATCH_SIZE, 1)))


























 32/128 [======>.......................] - ETA: 0s










Out[64]:








3.9920437335968018

























Training













In [70]:



    


for epoch in range(3*200):

    set_trainable(ratio_estimator, False)

    for _ in range(1):

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        metrics_inference = inference.train_on_batch(eps, np.tile(y, reps=(BATCH_SIZE, 1)))

    set_trainable(discriminator, True)

    for _ in range(3*50):

        w_sample_prior = prior.rvs(size=BATCH_SIZE)

        eps = np.random.randn(BATCH_SIZE, NOISE_DIM)
        w_sample_posterior = inference.predict(eps)

        inputs = np.vstack((w_sample_prior, w_sample_posterior))
        targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

        metrics_discrim = discriminator.train_on_batch(inputs, targets)

















In [71]:



    


inputs = np.vstack((w_sample_prior, w_sample_posterior))
targets = np.hstack((np.zeros(BATCH_SIZE), np.ones(BATCH_SIZE)))

















In [72]:



    


metrics = discriminator.evaluate(inputs, targets)


























 32/256 [==>...........................] - ETA: 0s


















In [73]:



    


w_grid_ratio = ratio_estimator.predict(w_grid.reshape(300*300, 2))
w_grid_ratio = w_grid_ratio.reshape(300, 300)

















In [74]:



    


fig, ax = plt.subplots(figsize=(5, 5))

ax.contourf(w1, w2, w_grid_ratio, cmap='magma')

ax.scatter(*inputs.T, c=targets, alpha=.8, cmap='coolwarm')

train_info = dict(zip(discriminator.metrics_names, metrics))

props = dict(boxstyle='round', facecolor='w', alpha=0.5)

ax.text(0.05, 0.05, 
        ('accuracy: {binary_accuracy:.2f}\n'        
         'loss: {loss:.2f}').format(**train_info), 
        transform=ax.transAxes, bbox=props)

ax.set_xlabel('$w_1$')
ax.set_ylabel('$w_2$')

ax.set_xlim(w_min, w_max)
ax.set_ylim(w_min, w_max)

plt.show()